WaveletComp (version 1.0)

wt: Wavelet transformation, and a simulation algorithm

Description

This function provides Morlet wavelet transformation results of the given time series, performed within the lower-order function WaveletTransform, subject to criteria concerning the time and frequency resolution, and an (optional) lower and/or upper Fourier period. It performs a simulation algorithm to test against a specified alternative hypothesis, which can be chosen from a variety of options, and provides p-values. The selected model will be fitted to the data and simulated according to estimated parameters in order to provide surrogate time series. This function is called by function analyze.wavelet.

The name and parts of the layout were inspired by a similar function developed by Huidong Tian and Bernard Cazelles (archived R package WaveletCo). The major part of the code for the computation of the cone of influence, and the code for Fourier-randomized surrogate time series has been adopted from Huidong Tian.

Usage

wt(x, start = 1, dt = 1, dj = 1/20, 
   lowerPeriod = 2*dt, upperPeriod = floor(length(x)*dt/3), 
   make.pval = T, method = "white.noise", params = NULL, 
   n.sim = 100, save.sim = F)

Arguments

x

the time series to be analyzed

start

starting value (in time units) at the time axis (for the computation of the cone of influence)

dt

time resolution, i.e. sampling resolution on time domain, 1/dt = number of intervals per time step. Default: 1.

dj

frequency resolution, i.e. sampling resolution on frequency domain, 1/dj = number of suboctaves (voices per octave). Default: 1/20.

lowerPeriod

lower Fourier period (in time units) for wavelet decomposition. Default: 2*dt.

upperPeriod

upper Fourier period (in time units) for wavelet decomposition. Default: (floor of one third of time series length)*dt.

make.pval

Compute p-values? Logical. Default: TRUE

method

the method of generating surrogate time series, select from: rlll{ "white.noise" : white noise "shuffle" : shuffling the given time series "Fourier.rand" : time series with a similar

params

a list of assignments between methods (AR, and ARIMA) and lists of parameter values which apply to surrogates. Default: NULL. Default includes: AR: AR = list(p=1), where:

n.sim

number of simulations. Default: 100

save.sim

Should simulations be saved on the output list? Logical. Default: FALSE.

Value

• A list with the following elements:
• Wave
  complex wavelet transform of the series
• Phase
  phases
• Ampl
  amplitudes
• Power
  wavelet power in the time/frequency domain
• Power.avg
  vector of average wavelet power in the frequency domain (averages over time)
• Power.pval
  p-values of wavelet power
• Power.avg.pval
  vector of p-values of average wavelet power
• Period
  the Fourier periods (in time units)
• Scale
  the scales
• coi.1, coi.2
  borders of the region where the wavelet transforms are not influenced by edge effects (cone of influence)
• nc
  number of columns/time steps
• nr
  number of rows/scales/Fourier periods
• axis.1
  tick levels corresponding to time steps
• axis.2
  tick levels corresponding to Fourier periods (= log2(Period))
• series.sim
  a data frame of the series which have been simulated as surrogates for the (detrended) time series (if both make.pval = TRUE and save.sim = TRUE.)

References

Aguiar-Conraria L., and Soares M.J., 2011. The Continuous Wavelet Transform: A Primer. NIPE Working Paper Series 16/2011.

Carmona R., Hwang W.-L., and Torresani B., 1998. Practical Time Frequency Analysis. Gabor and Wavelet Transforms with an Implementation in S. Academic Press, San Diego.

Cazelles B., Chavez M., Berteaux, D., Menard F., Vik J.O., Jenouvrier S., and Stenseth N.C., 2008. Wavelet analysis of ecological time series. Oecologia 156, 287--304.

Liu Y., Liang X.S., and Weisberg R.H., 2007. Rectification of the Bias in the Wavelet Power Spectrum. Journal of Atmospheric and Oceanic Technology 24, 2093--2102.

Tian, H., and Cazelles, B., 2012. WaveletCo. Available at http://cran.r-project.org/src/contrib/Archive/WaveletCo/, archived April 2013; accessed July 26, 2013.

Torrence C., and Compo G.P., 1998. A practical guide to wavelet analysis. Bulletin of the American Meteorological Society 79 (1), 61--78.

See Also

WaveletTransform, analyze.wavelet